Static output feedback problem for Lipschitz nonlinear systems

The output feedback stabilization of Lipschitz nonlinear systems is addressed. The synthesis of reduced-order controller is formulated as static output feedback problem. Based on coupled algebraic Riccati inequalities, the stability analysis of closed loop dynamic is presented. By utilizing some structural knowledge of Lipschitz nonlinearity, the sufficient conditions to obtain static as well as dynamic output feedback gains are given. For the class of Lipschitz nonlinearity, it is shown that the proposed condition is a necessary and sufficient condition to achieve static gain. The cone complementary linearization method is then applied to satisfy the proposed stability condition and to obtain an output feedback regulator. The effectiveness of proposed method is finally demonstrated through simulation results on some practical systems.